I need help with a problem from number theory (3) Show that (a + bi)P = (a – bi). Hint: for any x, y in a field containing Fp, (x + y)P = xP + yP.%3D(4) The norm of an element a + bi in F,[i] isN(a + bi) = (a + bi)(a – bi) = a² + b² e F,Show that for r, y e Fp[i], N(xy) = N (x)N(y).(5) Deduce from (3) that N(a + bi) = (a + bi)P+l1

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3) Show that (a + bi)º = (a – bi). Hint: for any x, y in a field containing Fp, (x+y)º = xº + yP. %3D

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.2: Integral Domains And Fields

Problem 24E: If a0 in a field F, prove that for every bF the equation ax=b has a unique solution x in F. [Type...

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Question

I need help with a problem from number theory

(3) Show that (a + bi)P = (a – bi). Hint: for any x, y in a field containing Fp, (x + y)P = xP + yP.
%3D
(4) The norm of an element a + bi in F,[i] is
N(a + bi) = (a + bi)(a – bi) = a² + b² e F,
Show that for r, y e Fp[i], N(xy) = N (x)N(y).
(5) Deduce from (3) that N(a + bi) = (a + bi)P+l
1

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